7.1.5 Gravitational Field Strength in a Radial Field

• The gravitational field strength, g at a point describes how strong or weak a gravitational field is at that point
• g in a radial field (such as a planet) is calculated using the equation:

• Where:
  • g = gravitational field strength (N kg^-1)
  • G = Newton’s Gravitational Constant
  • M = mass of the body producing the gravitational field (kg)
  • r = distance from the mass where you are calculating the field strength (m)

• Gravitational field strength, g, is a vector quantity
• The direction of g is always towards the centre of the body creating the gravitational field
  • This is the same direction as the gravitational field lines

• On the Earth’s surface, g has a constant value of 9.81 N kg^-1
• However, outside the Earth’s surface, g is not constant
  • g decreases as r increases by a factor of 1/r²
  • This is an inverse square law relationship with distance

• When g is plotted against the distance from the centre of a planet, r has two parts:
  • When r < R, the radius of the planet, g is directly proportional to r
  • When r > R, g is inversely proportional to r² (this is an ‘L’ shaped curve and shows that g decreases rapidly with increasing distance r)

Graph showing how gravitational field strength varies at greater distance from the Earth’s surface

• Sometimes, g is referred to as the ‘acceleration due to gravity’ with units of m s^-2
  • Any object that falls freely in a uniform gravitational field on Earth has an acceleration of 9.81 m s^-2